<PAGE>   1
================================================================================

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                             ----------------------

                                    FORM 10-Q

[X]               QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                 For the quarterly period ended MARCH 31, 1999

                                       OR

[ ]              TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                     For the transition period from      to
                                                    -----  ----

                         Commission file number 1-10934

                        LAKEHEAD PIPE LINE PARTNERS, L.P.
             (Exact name of Registrant as specified in its charter)

               DELAWARE                                      39-1715850     
    (State or other jurisdiction of                      (I.R.S. Employer  
    incorporation or organization)                       Identification No.)
                                                          
               
                               LAKE SUPERIOR PLACE
                             21 WEST SUPERIOR STREET
                              DULUTH, MN 55802-2067
              (Address of principal executive offices and zip code)

                                (218) 725-0100
              (Registrant's telephone number, including area code)

                             ----------------------

Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the Registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes X   No
                                             ----  

The Registrant had 24,990,000 Class A Common Units outstanding as at May 14,
1999.

================================================================================




<PAGE>   2




                                TABLE OF CONTENTS
<TABLE>
<CAPTION>
                                                                                                          PAGE
                                                                                                          ----
                          PART I. FINANCIAL INFORMATION
<S>       <C>                                                                                             <C>
ITEM 1.   Financial Statements

            Consolidated Statement of Income
              for the three month periods ended March 31, 1999 and 1998..............................       1

            Consolidated Statement of Cash Flows
              for the three month periods ended March 31, 1999 and 1998..............................       2

            Consolidated Statement of Financial Position
              as at March 31, 1999 and December 31, 1998.............................................       3

            Consolidated Statement of Partners' Capital
              for the three month period ended March 31, 1999........................................       4

            Notes to Consolidated Financial Statements...............................................       4

ITEM 2.   Management's Discussion and Analysis of
            Financial Condition and Results of Operations............................................       6

ITEM 3.   Quantitative and Qualitative Disclosures About Market Risk.................................       9


                           PART II. OTHER INFORMATION

ITEM 1.   Legal Proceedings..........................................................................      10

ITEM 6.   Exhibits and Reports on Form 8-K...........................................................      11

SIGNATURE ...........................................................................................      12
</TABLE>


      This Quarterly Report on Form 10-Q contains forward-looking statements.
These statements are based on the Partnership's beliefs as well as assumptions
made by and information currently available to the Partnership. When used in
this document, the words "anticipate," "believe," "expect," "estimate,"
"forecast," "project," and similar expressions identify forward-looking
statements. These statements reflect the Partnership's current views with
respect to future events and are subject to various risks, uncertainties and
assumptions including: 

      -   the Partnership's dependence upon adequate supplies of and demand for
          western Canadian crude oil,

      -   the price of crude oil and the willingness of shippers to ship crude
          oil when prices are low,

      -   the Partnership's ability to complete Year 2000 readiness activities,
          and

      -   the effects of competition, in particular, by other pipeline systems.

If one or more of these risks or uncertainties materialize, or should underlying
assumptions prove incorrect, actual results may vary materially from those
described in this Form 10-Q. Except as required by applicable securities laws,
the Partnership does not intend to update these forward-looking statements. For
additional discussion of such risks, uncertainties and assumptions, see the
Partnership's 1998 Annual Report on Form 10-K.



<PAGE>   3
--------------------------------------------------------------------------------

PART I - FINANCIAL INFORMATION
--------------------------------------------------------------------------------

ITEM 1.  FINANCIAL STATEMENTS
--------------------------------------------------------------------------------


                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                        CONSOLIDATED STATEMENT OF INCOME

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                              Three months ended
                                                                   March 31,
(unaudited; dollars in millions, except per Unit amounts)     1999          1998
--------------------------------------------------------------------------------

<S>                                                       <C>            <C>    
Operating Revenue                                         $   74.0       $  72.9
--------------------------------------------------------------------------------

Expenses
   Power                                                      13.5          17.7
   Operating and administrative                               13.8          16.8
   Depreciation (Note 3)                                      13.5          10.4
--------------------------------------------------------------------------------

                                                              40.8          44.9
--------------------------------------------------------------------------------

Operating Income                                              33.2          28.0

Interest and Other Income                                      1.5           2.9

Interest Expense                                             (12.7)         (7.7)

Minority Interest                                             (0.3)         (0.3)
--------------------------------------------------------------------------------

Net Income                                                $   21.7       $  22.9
================================================================================




Net Income Per Unit (Note 4)                              $    0.75      $  0.80
================================================================================


Cash Distributions Paid Per Unit (Note 5)                 $    0.86      $  0.78
================================================================================
</TABLE>


See accompanying notes to the consolidated financial statements.





                                       1
<PAGE>   4

--------------------------------------------------------------------------------

                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                      CONSOLIDATED STATEMENT OF CASH FLOWS

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                      Three months ended
                                                                           March 31,
(unaudited; dollars in millions)                                       1999         1998
----------------------------------------------------------------------------------------
<S>                                                                  <C>        <C>     
Cash Provided from Operating Activities
   Net income                                                        $  21.7    $   22.9
   Adjustments to reconcile net income to
     cash provided from operating activities:
        Depreciation                                                    13.5        10.4
        Interest on accrued rate refunds (Note 6)                        0.3         0.7
        Minority interests                                               0.3         0.3
        Other                                                            0.4         0.1
        Changes in operating assets and liabilities:
           Accounts receivable and other                                (2.7)        4.8
           Materials and supplies                                       (0.1)       (0.1)
           General Partner and affiliates                               (5.3)       (3.8)
           Accounts payable and other                                   (4.0)        3.5
           Interest payable                                             10.5         7.2
           Property and other taxes                                      2.1         3.0
           Payment of rate refunds and related interest (Note 6)        (7.3)       (7.2)
----------------------------------------------------------------------------------------


                                                                        29.4        41.8
----------------------------------------------------------------------------------------

Investing Activities
   Additions to property, plant and equipment                          (17.3)      (81.8)
   Short-term investments, net                                           -          36.4
   Advances to affiliate                                                 -          (6.9)
   Changes in construction payables                                    (34.8)       (3.1)
----------------------------------------------------------------------------------------


                                                                       (52.1)      (55.4)
----------------------------------------------------------------------------------------

Financing Activities
   Variable rate financing, net                                         20.0         -
   Loan from General Partner                                            25.0         -
   Distributions to partners                                           (24.5)      (21.8)
   Minority interest                                                    (0.3)       (0.2)
----------------------------------------------------------------------------------------

                                                                        20.2       (22.0)
----------------------------------------------------------------------------------------

Decrease in Cash and Cash Equivalents *                                 (2.5)      (35.6)

Cash and Cash Equivalents at Beginning of Period                        47.0       118.6
----------------------------------------------------------------------------------------

Cash and Cash Equivalents at End of Period                           $  44.5    $   83.0
========================================================================================
</TABLE>


* Cash equivalents are defined as all highly marketable securities with a
  maturity of three months or less when purchased. Short-term investments are
  marketable securities with a maturity of more than three months when
  purchased.

See accompanying notes to the consolidated financial statements.


                                       2
<PAGE>   5


--------------------------------------------------------------------------------

                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                  CONSOLIDATED STATEMENT OF FINANCIAL POSITION

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                              March 31,    December 31,
(unaudited, except for December 31, 1998; dollars in millions)                  1999          1998
-------------------------------------------------------------------------------------------------------

                                     ASSETS
<S>                                                                        <C>           <C>       
Current Assets
   Cash and cash equivalents                                               $     44.5    $     47.0
   Due from General Partner and affiliates                                        2.4           -
   Advances to affiliate                                                         32.0          32.0
   Accounts receivable and other                                                 27.9          25.2
   Materials and supplies                                                         7.2           7.1
---------------------------------------------------------------------------------------------------


                                                                                114.0         111.3
---------------------------------------------------------------------------------------------------


Deferred Charges and Other                                                        6.5           6.9
---------------------------------------------------------------------------------------------------


Property, Plant and Equipment
   At cost                                                                    1,504.3       1,487.3
   Accumulated depreciation                                                    (204.3)       (191.1)
---------------------------------------------------------------------------------------------------


                                                                              1,300.0       1,296.2
---------------------------------------------------------------------------------------------------


                                                                           $  1,420.5    $  1,414.4
===================================================================================================


                        LIABILITIES AND PARTNERS' CAPITAL
Current Liabilities
   Due to General Partner and affiliates                                   $      -      $      2.9
   Accounts payable and other                                                    14.5          53.3
   Interest payable                                                              16.0           5.5
   Property and other taxes                                                      14.0          11.9
   Accrued rate refunds and related interest (Note 6)                            21.7          28.7
---------------------------------------------------------------------------------------------------


                                                                                 66.2         102.3

Long-Term Debt                                                                  834.5         814.5
Loan from General Partner                                                        25.0           -
Minority Interest                                                                 2.6           2.6
Contingencies (Note 7)
---------------------------------------------------------------------------------------------------


                                                                                928.3         919.4
---------------------------------------------------------------------------------------------------


Partners' Capital
   Class A Common Unitholders
       (Units authorized and issued - 22,290,000) (Note 8)                      450.5         453.4
   Class B Common Unitholder (Units authorized and issued - 3,912,750)           37.3          37.3
   General Partner                                                                4.4           4.3
---------------------------------------------------------------------------------------------------


                                                                                492.2         495.0
---------------------------------------------------------------------------------------------------


                                                                           $  1,420.5    $  1,414.4
===================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.


                                       3
<PAGE>   6


--------------------------------------------------------------------------------

                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                   CONSOLIDATED STATEMENT OF PARTNERS' CAPITAL

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>

                                                        Class A             Class B
(unaudited, except for December 31, 1998;               Common              Common           General
 dollars in millions)                                 Unitholders          Unitholder        Partner            Total
---------------------------------------------------------------------------------------------------------------------

<S>                                                  <C>                   <C>              <C>                <C>   
Partners' Capital at December 31, 1998               $   453.4             $    37.3        $  4.3             $495.0

Net Income Allocation                                     16.3                   3.3           2.1               21.7

Distributions to Partners                                (19.2)                 (3.3)         (2.0)             (24.5)
---------------------------------------------------------------------------------------------------------------------

Partners' Capital at March 31, 1999                  $   450.5             $    37.3        $  4.4             $492.2
=====================================================================================================================
</TABLE>



See accompanying notes to the consolidated financial statements.


--------------------------------------------------------------------------------

           NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

--------------------------------------------------------------------------------

1.   Basis of Presentation

     The accompanying unaudited consolidated financial statements have been
     prepared in accordance with United States generally accepted accounting
     principles for interim financial information and with the instructions to
     Form 10-Q and Rule 10-01 of Regulation S-X. Accordingly, they do not
     include all the information and footnotes required by generally accepted
     accounting principles for complete financial statements. In the opinion of
     management, they contain all adjustments which management considers
     necessary to present fairly the financial position as at March 31, 1999 and
     December 31, 1998; the results of operations for the three month periods
     ended March 31, 1999 and 1998; and cash flows for the three month periods
     ended March 31, 1999 and 1998. The results of operations for the three
     months ended March 31, 1999 should not be taken as indicative of the
     results to be expected for the full year. The interim financial statements
     should be read in conjunction with the Partnership's consolidated financial
     statements and notes thereto presented in the Partnership's 1998 Annual
     Report on Form 10-K.

2.   Comparative Amounts

     Certain comparative amounts are reclassified to conform with the current
     quarter's financial statement presentation.

3.   Depreciation Rates

     Revised depreciation rates were filed with the Federal Energy Regulatory
     Commission ("FERC") to be effective on January 1, 1999, better representing
     the expected remaining service life of the pipeline system and coinciding
     with the in-service date for the System Expansion Program II ("SEP II").
     Depreciation expense for the three-months ended March 31, 1999, is $1.6
     million lower than it would have been under previous depreciation rates.


                                       4
<PAGE>   7


4.   Net Income Per Unit

     Net income per unit is computed by dividing net income, after deduction of
     the General Partner's allocation, by the weighted average number of Class A
     and Class B Common Units outstanding. The General Partner's allocation is
     equal to an amount based upon its 1% general partner interest, adjusted to
     reflect an amount equal to incentive distributions and an amount required
     to reflect depreciation on the General Partner's historical cost basis for
     assets contributed on formation of the Partnership. Net income per unit was
     determined as follows:

<TABLE>
<CAPTION>
-------------------------------------------------------------------------------------------------------------------

     Three months ended March 31,                                                            1999              1998
-------------------------------------------------------------------------------------------------------------------
<S>                                                                                     <C>                 <C>    
     Net income                                                                         $    21.7           $  22.9
-------------------------------------------------------------------------------------------------------------------

     Net income allocated to General Partner                                                 (0.2)             (0.2)

     Incentive distributions and historical cost depreciation adjustments                    (1.9)             (1.8)
-------------------------------------------------------------------------------------------------------------------

                                                                                             (2.1)             (2.0)
-------------------------------------------------------------------------------------------------------------------

     Net income allocable to Common Units                                               $    19.6           $  20.9
===================================================================================================================

     Common Units outstanding (millions)                                                     26.2              26.2
===================================================================================================================

     Net income per unit                                                                $    0.75           $  0.80
===================================================================================================================
</TABLE>

5.   Cash Distribution

     On April 15, 1999, the Board of Directors of the General Partner declared a
     cash distribution for the quarter ended March 31, 1999, of $0.875 per unit.
     The distribution will be made on May 14, 1999, to Unitholders of record on
     April 30, 1999.

6.   Accrued Rate Refunds and Related Interest

     In 1996, FERC approved a settlement agreement ("Settlement Agreement")
     between the Partnership and customer representatives on all outstanding
     contested tariff rates. The Settlement Agreement resulted in an approximate
     tariff rate reduction of 6% and total rate refunds and related interest of
     $120.0 million through the effective date of October 1, 1996. The $21.7
     million total rate refund balance remaining at March 31, 1999 is being
     repaid through a 10% reduction in tariff rates. This reduction will
     continue until all refunds have been made, which is expected to occur
     during the fourth quarter of 1999. Interest will continue to accrue on the
     unpaid balance based on the 90-day Treasury bill rate.

7.   Environmental Contingencies

     The Partnership is subject to federal and state laws and regulations
     relating to the protection of the environment. Environmental risk is
     inherent to liquid pipeline operations and the Partnership could, at times,
     be subject to environmental cleanup and enforcement actions. The General
     Partner manages this environmental risk through appropriate environmental
     policies and practices to minimize the impact to the Partnership. To the
     extent that the Partnership is unable to recover environmental costs in its
     rates (if not covered through insurance), the General Partner has agreed to
     indemnify the Partnership from and against any costs relating to
     environmental liabilities associated with the pipeline system prior to its
     transfer to the Partnership in 1991. This excludes any liabilities
     resulting from a change in laws after such transfer. The Partnership
     continues to voluntarily investigate past leak sites for the purpose of


                                       5
<PAGE>   8

     assessing whether any remediation is required in light of current
     regulations, and to date no material environmental risks have been
     identified.

8.   Common Units

     On April 28, 1999, the Partnership issued an additional 2,700,000 Class A
     Common Units, increasing the total number of Class A Common Units
     outstanding to 24,990,000, which, combined with the General Partner's
     contribution, provided net proceeds of approximately $119.7 million.
     Proceeds were used to repay indebtedness incurred under the Partnership's
     Revolving Credit Facility.

     Prior to this additional issuance of Class A Common Units, the General
     Partner held a 1% general partner interest and 14.8% limited partner
     interest in the Partnership, as well as a 1% general partner interest in
     Lakehead Pipe Line Company, Limited Partnership (the "Operating
     Partnership"). This resulted in an effective 16.6% combined interest in the
     Partnership by the General Partner. The Partnership owns a 99% limited
     interest in the Operating Partnership.

     Subsequent to this additional issuance of Class A Common Units, the General
     Partner has a 1% general partner and 13.4% limited partner interest in the
     Partnership, as well as a 1% general partner interest in the Operating
     Partnership. This results in an effective 15.3% combined interest in the
     Partnership.

--------------------------------------------------------------------------------

ITEM 2.    MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
           RESULTS OF OPERATIONS

--------------------------------------------------------------------------------

RESULTS OF OPERATIONS

Net income for the first quarter of 1999 was $21.7 million, or $0.75 per unit,
compared with 1998 first quarter net income of $22.9 million, or $0.80 per unit,
a decrease of $1.2 million, or $0.05 per unit. The decrease in net income was
primarily due to higher interest expense, partially offset by lower operating
expenses.

Operating revenue for the first quarter of 1999 was approximately the same as
first quarter 1998 as a decline in deliveries was largely offset by increased
tariffs effective January 1, 1999. Deliveries averaged 1,394,000 barrels per day
for the first quarter of 1999, down 12% from the 1,588,000 averaged for the
first quarter of last year. This decrease stems primarily from low crude oil
prices since mid-1998, which reduced the supply of crude oil available to the
Partnership. First quarter deliveries were also adversely impacted by the
process of filling new lines with crude oil and by maintenance activities at a
number of refinery sites. The Partnership expects that average daily deliveries
for 1999 will be approximately 1.5 million barrels per day, which is consistent
with the estimate made in December 1998. System utilization, measured in barrel
miles, was 89 billion for the first quarter of 1999, as compared to 99 billion
for last year's first quarter, reflecting decreased deliveries by the
Partnership.

Total operating expenses for the first quarter of 1999 decreased $4.1 million,
or 9.1%, from the corresponding period of 1998. The decline resulted from lower
power costs associated with reduced deliveries and lower operating and
administrative costs due to cost control efforts by the Partnership and timing
of maintenance activities. These savings were partially offset by increased
depreciation expense resulting from the placing in service of SEP II. The
depreciation expense increase was somewhat offset by revised depreciation rates
filed with FERC to be effective on January 1, 1999, to better represent the
expected remaining service life of the pipeline system and to coincide with the
in-service date for SEP II. Depreciation expense for the three-months ended
March 31, 1999, is $1.6 million lower than it would have been under previous
depreciation rates.

Interest and other income for the first three months of 1999 was $1.4 million
less than the same period in 

                                       6
<PAGE>   9

1998 primarily due to lower interest income from lower cash balances as a result
of SEP II and Terrace (see " - General, - Terrace Program") capital
expenditures. Interest expense increased $5.0 million due to higher borrowings
associated with the Partnership's expansion projects.

LIQUIDITY AND CAPITAL RESOURCES

The Partnership anticipates that it will continue to have adequate liquidity to
fund future recurring operating, investing and financing activities. The
Partnership intends to fund the remaining portion of Terrace (see " - General, -
Terrace Program") and ongoing capital expenditures with the proceeds from future
equity and debt offerings, borrowings, cash generated from operating activities,
and existing cash and cash equivalents. Cash distributions are expected to be
funded with internally generated cash. The Partnership's ability to make future
debt and equity offerings will depend on prevailing market conditions and
interest rates and the then-existing financial condition of the Partnership.

At March 31, 1999, cash and cash equivalents totaled $44.5 million, as compared
to $47.0 million at December 31, 1998, as cash required for distributions and
capital expenditures slightly exceeded cash generated from operating activities
and borrowings under the Partnership's Revolving Credit Facility and from the
General Partner. Of this $44.5 million, $25.3 million ($0.875 per unit) will be
used for the cash distribution payable May 15, 1999, with the remaining $19.2
million available for capital expenditures or other business needs.

Due to changes in working capital, cash flow from operating activities for the
first quarter of 1999 was $29.4 million, as compared with $41.8 million for the
same period last year.

In late March 1999, the Partnership borrowed $25 million from the General
Partner under an arrangement pursuant to which the General Partner is authorized
to make loans from time to time to the Partnership, on an uncommitted basis, in
an amount not to exceed $200 million. Interest on the loan accrued at a rate of
7.75%. This loan was repaid in early April.

On April 28, 1999, the Partnership issued an additional 2,700,000 Class A Common
Units, increasing the total number of Class A Common Units outstanding to
24,990,000, which, combined with the General Partner's contribution, provided
net proceeds of approximately $119.7 million. Proceeds were used to repay
indebtedness incurred under the Partnership's Revolving Credit Facility.

Capital expenditures for the first quarter of 1999 totaled $17.3 million, of
which $14.0 million was for the first phase of the Terrace program (see " -
General, - Terrace Program"). The first phase of the Terrace program is largely
complete with $126.7 million of the anticipated $138.0 million total capital
expenditures incurred through March 31, 1999. In addition to Terrace, the
Partnership anticipates spending approximately $8.2 million for pipeline system
enhancements and $13.5 million for core maintenance activities in 1999.
Additional capital expenditures for SEP II will be incurred for minor
restoration and clean-up work and finalization of rights-of-way costs. It is not
anticipated that these expenditures will be material in comparison to the $450
million cost of the project.

GENERAL

Year 2000 Issue
---------------

The Year 2000 Readiness Program, which is being undertaken jointly by the
Partnership and its Enbridge affiliates, continued on schedule, having attained
several milestone points by March 31, 1999. Remediation, testing and deployment
of critical systems that control the flow of crude oil and natural gas liquids
in the Partnership's pipeline system are on target for completion by June 30,
1999.

In order to address unforeseen year 2000 problems that could arise and in an
attempt to minimize business disruptions, the Partnership is developing business
continuity plans for all critical processes, systems, 


                                       7
<PAGE>   10

technologies and external relationships. These plans are expected to be
completed by mid 1999. As part of the continuity planning process, significant
external relationships are being investigated. The most significant of these
relationships are reliance on electrical and telecommunication suppliers as well
as connecting pipelines and refineries.

For additional discussion of the year 2000 issue, see the Partnership's 1998
Annual Report on Form 10-K.

Terrace Program
---------------

The Terrace program, which is being undertaken by the Partnership in conjunction
with Enbridge Pipelines Inc. ("Enbridge Pipelines"), the parent company of the
General Partner, is a multi-phased expansion program. Subject to continued
industry support, customer requirements and receipt of regulatory approvals,
this multi-phased expansion program is expected to be completed over the period
1999 through 2005.

Phase I of the Terrace expansion program includes construction of new 36-inch
diameter pipeline facilities from Kerrobert, Saskatchewan, to Clearbrook,
Minnesota, which began in September 1998. The new pipeline will join existing
48-inch pipeline loops between Kerrobert and Clearbrook, creating another
separate pipeline joining those locations. Phase I of the Terrace Program will
be completed in two stages during 1999 and is expected to provide 170,000
barrels per day of added heavy crude oil capacity from the Canadian border to
Superior, Wisconsin by September 1999. Of this additional capacity,
approximately 95,000 barrels per day should be available during the second
quarter of this year. Phase I is anticipated to cost the Partnership $138
million in the U.S., and to cost Enbridge Pipelines Cdn. $610 million in Canada.
The Partnership expects that it will spend approximately $25.3 million on its
portion of Terrace during 1999.

Subsequent to the completion of all phases of Terrace, and after allowing for
anticipated declines in light crude oil production, total system delivery
capability is expected to increase by approximately 350,000 barrels per day.

Tariff Matters
--------------

The Partnership filed a tariff agreement ("Tariff Agreement") with FERC
providing for tariff rate surcharges commencing as of January 1, 1999 (with
respect to SEP II) and April 1, 1999 (with respect to Terrace). This filing
consolidated the Partnership's 1996 settlement agreement ("Settlement
Agreement") with respect to SEP II and other significant agreements with
customers concerning Terrace and the transportation of heavy crude oil. FERC
approved the Tariff Agreement, which allows the Partnership to earn a return on
its SEP II equity investment that varies with utilization of SEP II capacity on
Enbridge Pipelines' system. Under the Tariff Agreement, return on SEP II equity
can range from a minimum of 7.5% to a maximum of 15%.

Under the Tariff Agreement, the tariff rate surcharge for SEP II is
approximately $0.11 per barrel for light crude oil to Chicago, Illinois. This
surcharge allows the Partnership to recover the cost of service for SEP II
facilities and earn a 7.5% return on SEP II equity investment during 1999.

The tariff rate surcharge for Terrace is approximately $0.013 per barrel for
light crude oil to Chicago. This tariff surcharge is based upon the assumption
that Phases II and III of Terrace will be completed. If these phases of Terrace
are not completed, the Tariff Agreement provides that the Partnership will be
allowed to increase the tariff surcharge on a cost of service basis to allow
recovery of, and return on, the Partnership's Phase I Terrace investment
including any revenue variances between the application of the toll increment
and the annual cost of service of Terrace.

Other Developments
------------------

Enbridge and its affiliates have also recently completed additional North
American crude oil pipeline projects. The Partnership believes that these
projects, even though they are not owned by the Partnership, are complementary
to and may result in increased deliveries on the Partnership's pipeline system.
Two of these 

                                       8
<PAGE>   11

projects are:

-    Enbridge Toledo - Enbridge has completed construction of a new pipeline
     that connects the Partnership's facilities at Stockbridge, Michigan to two
     refineries in the Toledo, Ohio area. This pipeline is anticipated to have
     capacity in excess of 80,000 barrels per day in heavy crude oil service and
     became available for service in early February 1999.

-    Enbridge Athabasca - In March 1999, Enbridge completed construction of a
     new 30-inch diameter pipeline for the delivery of heavy crude oil from the
     Athabasca oil sands region near Fort McMurray, Alberta to Hardisty,
     Alberta. At Hardisty, the Athabasca pipeline accesses other pipeline
     systems including Enbridge Pipelines' system in western Canada. This
     project provides new pipeline capacity to accommodate anticipated growth in
     crude oil production from the Athabasca oil sands region. When fully
     powered, the Athabasca pipeline is anticipated to have an ultimate capacity
     of approximately 570,000 barrels per day. Enbridge has entered into a
     30-year transportation arrangement with Suncor Energy Inc., the initial
     shipper on the pipeline.

--------------------------------------------------------------------------------

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET RISK

--------------------------------------------------------------------------------

The Partnership's market risk is primarily impacted by changes in interest
rates. The Partnership has minimal foreign exchange risk and its cash flows are
not significantly impacted by changes in commodity prices, as the Partnership
does not own the crude oil and NGL it transports. However, commodity prices have
a significant impact on the underlying supply and demand for crude oil and NGL
that the Partnership transports. The Partnership does not currently hold or
issue derivative instruments for trading or any other purposes.

The Partnership's market risk with respect to interest rate exposure is managed
through its long-term debt ratio target, and its allocation of fixed and
floating rate debt. Information about the Partnership's financial instruments
that are sensitive to changes in interest rates has not changed from that
presented in the Partnership's 1998 Annual Report on Form 10-K.














                                       9
<PAGE>   12



--------------------------------------------------------------------------------
PART II - OTHER INFORMATION
--------------------------------------------------------------------------------

ITEM 1.  LEGAL PROCEEDINGS
--------------------------------------------------------------------------------


In late July 1998, the Partnership's directional drilling operations for SEP II
construction caused a discharge of non-hazardous bentonite drilling mud in a
wetlands area. The State of Illinois is pursuing an action relating to this
discharge under Natural Resource Damage Assessment regulations of the Clean
Water Act to seek compensation for damage to the wetlands area. It is expected
that a settlement will be reached with the State to resolve the matter and that
it will not have a material impact on the financial condition of the
Partnership. The U.S. Environmental Protection Agency ("EPA") issued an
information request on April 6, 1999, seeking information regarding the
selection of the pipeline route through the wetlands area. The Partnership
responded to the information request on April 20, 1999. The EPA has also
informed the Partnership that it is preparing to file an administrative
complaint in the next several weeks seeking a civil administrative penalty for
violations of the Clean Water Act resulting from the bentonite discharges into
the wetlands.

The Illinois Attorney General is seeking payment of a penalty of $98,000 and
costs of $2,000 for a May 28, 1998, release of crude oil caused by a third party
in Orland Park, Illinois. The Partnership and the Attorney General are
negotiating the terms of a Consent Order to be entered by the Attorney General
with the concurrence of the Partnership, the General Partner, and the third
party.

The Partnership received a Notice of Violation, dated October 29, 1998, from the
Wisconsin Department of Natural Resources ("Wisconsin DNR") that alleges the
Partnership failed to monitor discharges of water from SEP II construction
trenches on certain occasions and exceeded the effluent limitations set forth in
a permit. The Partnership has submitted its reply to the notice and intends to
cooperate with the Wisconsin DNR in an effort to resolve the issue and any
penalties that may ensue. It is not anticipated that any penalty will have a
material impact on the financial condition of the Partnership.













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<PAGE>   13




--------------------------------------------------------------------------------

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K
--------------------------------------------------------------------------------


a)   Exhibits

     27.1 Financial Data Schedule as of and for the three months ended March 31,
     1999.

b)   Reports on Form 8-K

     A report on Form 8-K was filed on April 15, 1999, submitting an audited
     Consolidated Statement of Financial Position of Lakehead Pipe Line Company,
     Inc., the General Partner of Lakehead Pipe Line Partners, L.P., at December
     31, 1998 and 1997, together with the Report of Independent Public
     Accountants. A report on Form 8-K/A was filed on April 19, 1999, for the
     sole purpose of including the conformed signature that was inadvertently
     omitted from the original filing dated April 15, 1999.

     A report on Form 8-K was filed April 16, 1999, submitting a press release
     dated April 15, 1999, announcing an increase in cash distribution and first
     quarter financial results. A report on Form 8-K/A was filed on April 19,
     1999, for the sole purpose of including the conformed signature that was
     inadvertently omitted from the original filing dated April 16, 1999.

     A report on Form 8-K was filed April 26, 1999, submitting the final version
     of the Underwriting Agreement, entered into among the Partnership, the
     General Partner, Lakehead Pipe Line Company, Limited Partnership and the
     underwriters named therein in connection with the Partnership's public
     offering of 2,700,000 Class A Common Units, as well as a press release
     related thereto.












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<PAGE>   14




                                    SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.




                                            LAKEHEAD PIPE LINE PARTNERS, L.P.
                                                     (Registrant)

                               By:     Lakehead Pipe Line Company, Inc.
                                       as General Partner



                                                 /s/ M.A. Maki
                               -------------------------------------------------
                                                     M.A. Maki
                                                 Chief Accountant
                                        (Principal Financial and Accounting
                                          Officer and Authorized Officer)



                                               Dated:  May 14, 1999











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